basic rings

basic rings

The following rings are initially present in every session with Macaulay 2.

ZZ -- the class of all integers

QQ -- the class of all rational numbers

RR -- the class of all real numbers

CC -- the class of all complex numbers

(The names of these rings are double letters so the corresponding symbols with single letters can be used as variables in rings.) Entries of these rings are constructed as follows, and the usual arithmetic operations apply.

i2 : 123/4



     123

o2 = ---

      4



o2 : QQ

i3 : 123.4



o3 = 123.4



o3 : RR

i4 : 123+4*ii



o4 = 123 + 4ii



o4 : CC

The usual arithmetic operations are available.

i5 : 4/5 + 2/3



     22

o5 = --

     15



o5 : QQ

i6 : 10^20



o6 = 100000000000000000000

i7 : 3*5*7



o7 = 105

i8 : 5!



o8 = 120

An additional pair of division operations that produce integral quotients and remainders is available.

i9 : 1234//100



o9 = 12

i10 : 1234%100



o10 = 34